how to pass the record in read only grid through the record type?

You have to reference the record type in the "data" parameter and then reference each field using a record type field reference in your columns. For instance, your expression could look something like this:

a!gridField(
  label: "Read-Only Grid",
  labelPosition: "ABOVE",
  data: recordType!Timesheet,
  columns: {
    a!gridColumn(
      label: "Employer Name",
      sortField: recordType!Timesheet.fields.employerName,
      value: a!linkField(
        links: a!recordLink(
          label: fv!row[recordType!Timesheet.fields.employerName],
          recordType: recordType!Timesheet,
          identifier: fv!row[recordType!Timesheet.fields.employeeId]
        )
      )
    )
  }
)

You have to reference the record type in the "data" parameter and then reference each field using a record type field reference in your columns. For instance, your expression could look something like this:

a!gridField(
  label: "Read-Only Grid",
  labelPosition: "ABOVE",
  data: recordType!Timesheet,
  columns: {
    a!gridColumn(
      label: "Employer Name",
      sortField: recordType!Timesheet.fields.employerName,
      value: a!linkField(
        links: a!recordLink(
          label: fv!row[recordType!Timesheet.fields.employerName],
          recordType: recordType!Timesheet,
          identifier: fv!row[recordType!Timesheet.fields.employeeId]
        )
      )
    )
  }
)

Hi Peter, 
this is not redirect to summary page and edit employee time sheet.

What's the value of the "timesheetid" field in your data returned? Are you sure that data is populated (and does the ID there match an expected ID for your timesheet record)?